Energy of Stationary States Calculator

Energy of Stationary States Formula:

\[ E_n = [Rydberg] \times \frac{Z^2}{n^2} \]

Energy of Stationary States (J):

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1. What is Energy of Stationary States?

Definition: Energy of Stationary States is the energy at a quantum state with all observables independent of time.

Purpose: This calculator helps determine the energy levels of electrons in atoms using the Bohr model.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ E_n = [Rydberg] \times \frac{Z^2}{n^2} \]

Where:

\( E_n \) — Energy of stationary state (Joules)
\( [Rydberg] \) — Rydberg constant (10973731.6)
\( Z \) — Atomic number (number of protons)
\( n \) — Principal quantum number

Explanation: The energy depends on the atomic number squared and inversely on the square of the quantum number.

3. Importance of Energy Calculation

Details: Calculating stationary state energies helps understand atomic spectra, electron transitions, and quantum behavior.

4. Using the Calculator

Tips: Enter the atomic number (Z) and principal quantum number (n). Both must be positive integers.

5. Frequently Asked Questions (FAQ)

Q1: What is the Rydberg constant?
A: The Rydberg constant represents the limiting value of the highest wavenumber of any photon that can be emitted from hydrogen.

Q2: What are typical quantum numbers?
A: For hydrogen (Z=1), n=1 is the ground state, n=2 is the first excited state, etc.

Q3: Why does energy depend on Z²?
A: The energy scales with the square of the nuclear charge due to the Coulomb potential.

Q4: What units is the energy in?
A: The energy is calculated in Joules (J).

Q5: Can this be used for all atoms?
A: This formula works best for hydrogen-like atoms (single electron systems).